The biggest question is: to buy one now, or wait for the upcoming replacement?

It is really up to your needs. Here are my thoughts:

BUY NOW:

Prices are at their lowest. We may never see lower prices for these models before they get discontinued. In addition to the low prices, some stores add extras, like extra battery, camera bag, memory cards, etc.

The New models will be significantly more expensive. If we assume that they will keep the introductory price of the current models, this is still a good $800 savings. This could buy you a wonderful lens like the 20mm f/1.8, or the 24mm f/1.8, etc. If Nikon bump the price a bit – like $3499 for the D820 similarly to 5D Mark IV (currently $200 off), this is exactly $1000 more expensive than what D810 is now.

Nikon has the bad reputation to have some defects in their cameras right after release – look at D7000, D800/D800E, D600, D750, etc. Even the latest D500 had issues at the beginning. Pre-ordering such camera makes you a beta tester of some sorts. Are you willing to deal with problems if there are any?

It is the unknown of what the new model will be? IS it going to be an upgrade you waited for, or it will go in very different direction?

WAIT:

You will get the newest (latest and greatest) technology

You may get some new features and stay ahead of the competition

In conclusion, everyone knows his needs. If you think that the rumored new model will give you everything you want/need for your work, then wait for it. If you think that you can still put in good use the current models, I think now is the time to buy some. Years ago we couldn’t even dream to have an excellent Full Frame DSLR for under $1500, as D750 is now.
Let me know what do you think?